#### rock.freak667

Homework Helper

- 6,230

- 27

**1. The problem statement, all variables and given/known data**

[tex]f:\rightarrow x+1,g:x\rightarrow |x|[/tex]

Solve the equation gf(x)=fg(x)

**2. Relevant equations**

**3. The attempt at a solution**

gf(x)=|x+1|

and fg(x)=|x|+1

so I drew the graphs of y=gf(x) and y=fg(x) on the same axes.

For x<0 the graphs do not intersect as the two lines are parallel (having the same gradient) and hence there is no solution for x<0.

BUT, for x>0, the two lines are the same...so that means there are an infinite number of solutions for x>0. Does that mean I write the answer as {x:x>0} ?